Solving Quadratic Equations And Functions By Algebraic And Graphical Methods With Transformation.
This is a comprehensive course designed for adult or student not less than 18 years on quadratic equations, functions and transformations. In section one,we begin lecture one by introducing and defining quadratic equations, followed by finding the roots of a given quadratic equation. Also ,included in this first lecture and that leads us to solving quadratic equations using the method of completing the square.
We derived the general formula for solving a quadratic equation of all types. This included finding a quadratic equation when its roots are given with examples.
some word problems involving quadratic equation and function by graphical method is treated. This includes identification of quadratic equations and functions by shape and position of vertex point. To plot the graph of quadratic function or equation, we begin by finding the roots, y intercept and the turning point.
These are covered within the first body of lecture two. Also, basic derivative of gradient of functions is used. This makes it easy to find the turning point and plot the required graph from which the solutions of the equation are obtained.
Lecture three of section three includes solving quadratic equation by square root method followed by a method of factorization. These methods are elaborated much more in this lecture unlike introductory lecture one with more examples for total understanding of the course. Zeros of function and word problems leading to quadratic equations are included.
Transformation of quadratic functions is, extensively, covered in lecture four of section four. Terminologies associated with transformation that include shrink, shift, stretch, reflection and translation both in horizontal and vertical positions are included in this lecture four. Interpretation of transformation of parabolic function in vertex form, differences between horizontal and vertical translation are treated as well .
Finally,we end lecture four by writing a rule for the transformation of quadratic function and solve real life problems involving quadratic equations and functions.
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